X Chromosome Inactivation (XCI): The epigenetic process which silences one X chromosome in females
to achieve gene dosage balance between males and females. [1]

Xa: the active X chromosome

Xi: the inactive X chromosome

Xm: maternally inheritted X chromosome

Xp: paternally inheritted X chromosome

Figure 1: The paternally inherited (Xp) chromosome in and the maternally
inherited chromosome (Xm). The active chromosome Xa is represented with
color filled in, while the inactive chromosome Xi is represented with no color fill.

Escape: The status of genes which are expressed on Xi. These genes “escape” inactivation.

Inactive: The status of genes which are suppressed on Xi.

Variable: The status of genes which are expressed on Xi in some tissues/individuals,
but not in all tissues/individuals. [2]

Mosaicism: Xa and Xi are typically randomly assigned to either Xp or Xm in each
cell. Mosaicism refers to the heterogeneity of Xa/Xi assignment among a set of cells.

Figure 2: Mosaicism. A sample of six cells with differences in Xa/Xi assignments.

Skew: A ratio which represents the mosaicism of Xa/Xi assignment in a set of cells.

Figure 3a: Skew Ratio 1. Two samples have Xi assignment on Xm, while two samples
have Xi assignment on Xp. The resulting skew ratio is 50:50.

Figure 3b: Skew Ratio 2. Three samples have Xi assignment on Xm, while one sample
has Xi assignment on Xp. The resulting skew ratio is 25:75.

Figure 3c: Skew Ratio 2. All four samples have Xi assignment on Xm.
The resulting skew ratio is 0:100. This is a rare occurrence in nature,
and is often referred to has non-random assignment or fully skewed [3]

%Xi or tau (\(\tau\)): The ratio of a gene’s expression on Xi over its total expression across
both Xa and Xi, referred to as %Xi [4] or \(\tau\) [5]. In allele specific expression (ASE)
based methods for escape inference, \(\tau\) is compared to the skew ratio. Significant
deviation of \(\tau\) from the skew ratio reflects biallelic expression and classifies a gene as
escape.

\(N=expression\ level\)

\(j=gene\)

\(i=inactive\ x\ chromosome\)

\(a=active\ x\ chromosome\)

\(\tau = \frac{N_{ij}}{N_{aj} + N_{ij}}\)

A note about skew: For ASE based methods, data sets with a higher skew ratio (such as 25:75)
are strengthened for estimating escape expression due to the lower Xi expression levels
required to infer significance.

Tau+ (\(\tau\)+): The \(\tau\) (or %Xi) values from the subset of XCI calls which were inferred from
samples which were sufficiently skewed (>25:75). This subset is a more robust estimate of
ASE and is strengthened for escape calling. [4]